Vision Based Motion Estimation of Obstacles in

Dynamic Unstructured Environments

Andrei Vatavu and Sergiu Nedevschi,

Computer Science Department, Technical University of Cluj-Napoca,

26-28 G. Baritiu Street, Cluj-Napoca, Romania

{Andrei.Vatavu, Sergiu.Nedevschi}@cs.utcluj.ro

Abstract. Modeling static and dynamic traffic participants is an important

requirement for driving assistance. Reliable speed estimation of obstacles is an

essential goal especially when the surrounding environment is crowded and

unstructured. In this paper we propose a solution for real-time motion

estimation of obstacles by using the pairwise alignment of object delimiters.

Instead of involving the whole 3D point cloud, more compact polygonal models

are extracted from a classified digital elevation map and are used as input data

for the alignment process.

Keywords: Motion Estimation, Polygonal Map, Object Contour, Iterative

Closest Point, Driving Assistance, Stereo-Vision, Object Delimiters.

1 Introduction

In the context of Advanced Driver Assistance Systems, modeling static and dynamic

entities of the environment is a key problem. The detection of moving traffic

participants is an essential intermediate step for higher level driving technology tasks

such as collision warning and avoidance, path planning or parking assistance. The

problem of dynamic environment representation becomes even more difficult when

the surrounding world is unstructured and heterogeneous, including the cases of

crowded urban centers, traffic intersections or off-road scenarios. The representation

component may be influenced by several factors: noisy measurements, occlusions,

wrong data association or unpredictable nature of the traffic participants. In such

complex environments, a driver assistance system should be able to detect other

moving traffic entities in real-time and at a high accuracy.

Usually, the classic approaches of dynamic obstacles detection and tracking consist

in extracting a set of features from the scene and estimating the motion from their

displacement. Current solutions can directly use 3D points [1], or they can track high

level attributes such as 2D boxes or 3D cuboids [2], stixels [3], free-form polygonal

models [4], object contours [5][8] etc.

The dynamic obstacle modeling solutions can be classified by the nature of used

sensors. The most common used sensors are vision based [2], laser [6][7], sonar [9] or

radar. The motion estimation techniques are also distinguished by the level at which

the dynamic features detection is applied. Some of the existing methods rely on

computing motion before generating a model [10][12], while other methods are based

on extracting some attributes and subsequently estimating their dynamic parameters

[2][4][5].

Many of dynamic object detection solutions use intermediate representations as

primary information. A common practice is mapping 3D information into occupancy

grids [10], digital elevation maps [11] or octrees [9].

The data association and identifying correct correspondences steps play an

important role in estimating the motion of the traffic entities. One of the widely used

methods for model fitting in the presence of many data outliers is the RANSAC

algorithm [13]. However, its accuracy depends directly on the number of used

samples. This may lead to a high computational cost.

Direct matching solutions such as Iterative Closest Point (ICP) [14] algorithm are

most common for vehicle localization and mapping [4]. In [15] the convergence

performance for several ICP variants is compared. An optimized ICP method that

uses a constant time variant for finding the correspondences is presented. In [4] a

moving objects map is segmented by assuming that dynamic parts do not fulfill the

constraints of the SLAM. However, the most of scan matching methods do not take

into consideration the ego-motion parameters. The data association of objects in

subsequent scans is hard to be achieved when the traffic participants or the ego

vehicle moves at high speeds or when the measurement uncertainties are not taken

into account.

We propose a solution of representing the dynamic environment in real-time by

using the pairwise alignment of free-form delimiters and considering the advantages

provided by a stereovision system, by inheriting the object information from the

intermediate representation. Instead of registering the whole 3D point cloud, our

method is based on extracting the most visible object cells from the ego car and using

them as input data for the alignment process. We propose an extension of the classical

ICP algorithm by applying a set of improvement heuristics:

• The data association is one of the problems of the classical scan matching

techniques. It’s hard to estimate the correspondent models from previous scans

only based on the proximity criterion. In our case we introduce a pre-processing

step. First, we find the correspondence pairs between the model set (contour

extracted in previous frame) and the measurement set (current frame results) by

finding similarities between object blobs and passing this information at the

contour level. Then, a list of associated contour candidates is generated and is used

as the input for the next steps of the alignment;

• For the registration process we use free-form polygonal models that minimize the

erroneous results caused by occlusions, or by stereo reconstruction errors. The

main idea is that we are taking into account only the most visible points from the

ego-vehicle by performing a radial scanning of the environment [16];

• The previously extracted speeds are used as the initial guess for the ICP algorithm;

• In order to filter the alignment outliers, a rejection metric that includes stereo

uncertainties is proposed;

Our method is based on information provided by a Digital Elevation-Map, but can

be easily adapted for other types of intermediate representations.

The remaining of the paper is structured as follows: Section 2 introduces the

architecture of the proposed dynamic environment representation. Section 3 presents

the pre-processing module with a group of necessary tasks for extracting object

dynamic properties. In section 4, the main steps of the motion estimation component

are detailed. The last two sections show the experimental results and conclusion about

this contribution.

2 System Architecture

The dynamic environment representation method has been developed and adapted for

crowded environments such as urban city traffic scenes. In this paper we extend our

previous Dense Stereo-Based Object Recognition System (DESBOR) [22]. The

system architecture (see Fig. 1) could be divided in four main blocks: data acquisition

and 3D reconstruction, intermediate representation, pre-processing, and motion

estimation.

Fig. 1. System Architecture.

Data acquisition and 3D reconstruction is the first level of the processing flow.

At this stage the images are acquired from the two cameras, then the 3D

reconstruction is performed using a specialized TYZX [17] board. The resulted point

cloud is used as the input information for computing the Digital Elevation Map.

Intermediate representation: the raw dense stereo information is mapped into a

Digital Elevation Map (see Fig. 2). The resulted intermediate representation contains

three types of cells: road, traffic isle and object. The cells are labeled based on their

height information. More details about the Elevation Map are presented in [18].

Pre-processing: The pre-processing level groups a set of basic tasks that are

performed prior the ICP algorithm. At this phase, the object contours are extracted by

radial scanning of the Elevation Map. For the delimiters extraction we use the Border

Scanner algorithm previously developed by us [16]. We apply the ego-motion

compensation for the Elevation Map and contours that are extracted in previous

frame, assuming that we know the odometry information. The ego-vehicle motion is

compensated in order to separate its speed from the independent motion of the objects

in the traffic scene. Another pre-processing task is to associate the polygonal models.

The data association is achieved by using the maximum overlapping score of the

Elevation Map blobs. Considering that each polygonal model inherits the blob type, it

also inherits the blob association information.

Fig. 2. a) An urban traffic scene. b) The Elevation Map projected on the left camera image.

c) A compact representation of the environment. d) The top view of the Elevation Map. The

Elevation Map cells are classified (blue – road, yellow – traffic isle, red – obstacles).

Fig. 3. Coordinate System.

Motion Estimation: As the result of the pre-processing level, a list of candidates is

provided for the ICP module. Each candidate represents a pair of associated contours

in the previous stage. For each candidate, a rotation and a translation is estimated by

the ICP algorithm. Then the computed motion information is associated to the static

polygonal models. A dynamic polyline map is generated as the result. Each polyline

element is characterized by a set of vertices describing the polygon, position, height,

type (traffic isle, obstacle), orientation and magnitude.

In our case the two cameras are placed on a moving vehicle. We use a coordinate

system where the z axis points toward the direction of the ego-vehicle, and the x axis

is oriented to the right. The origin of the coordinate system is situated in front of the

car (see Fig. 3).

3 Pre-Processing Level

The pre-processing stage consists in performing necessary tasks prior the motion

estimation. First, extracting a sufficiently generic model is needed. The extracted

model should allow us the creation of fast subsequent algorithms and as well it should

minimize the representation errors caused by noisy 3D reconstruction or by

occlusions.

A second task is to separate the ego-vehicle speed from the independent motion of

the other objects in the traffic scene. This is achieved by compensating the ego

motion.

And finally, elevation map blob is labeled and is used in data association. As the

result a list of pairs of contours is extracted and is provided subsequently to the ICP

step. Thus, unlike the other classical methods that involve aligning the whole local

maps at once, and then segmenting the dynamic obstacles from the static ones, we

first associate the obstacles at the blob level and then apply the ICP for each

associated candidate.

3.1 Polyline-Based Environment Perception

For the polyline based object representation we use the Border Scanner algorithm

described by us in [16]. The main idea is that we are taking into account only the most

visible points from the ego car and extract object delimiters by radial scanning of the

Elevation Map. Our method is similar to a Ray-Casting approach. The proposed

method consists in determining the first occupied point intersected by a virtual ray

which extends from the ego-car position. The scanning axis moves in the radial

direction, having a fixed center at the ego-vehicle position (the coordinate system

origins). At each step we try to find the nearest visible point from the Ego Car situated

on the scanning axis. In this way, all subsequent cells Pi are accumulated into a

Contour List C, by moving the scanning axis in the radial direction:

},...,{ 21 nPPPC = (1)

For each object Oi described by a contour Ci we apply a polygonal approximation

of Ci by using a split-and-merge technique described in [19]. The extracted polygon is

used to build a compact 3D model based on the polyline set of vertices as well as on

the object height. A polyline based representation is described in Fig. 2.d.

3.2 Ego-Motion Compensation

Before estimating the motion of the traffic entities, the movement of the ego vehicle

must also be taken into consideration. In order to compensate the ego motion in the

successive frames, for each given point Pt-1(xt-1, yt-1, zt-1) in the previous frame, the

corresponding coordinates Pt(xt, yt, zt) in the current frame are computed by applying

the following transformation:

( )

+

=

−

−

−

zt

t

t

y

t

t

t

tz

y

x

R

z

y

x

0

0

1

1

1

ψ

(2)

Where ( )ψyR is the rotation matrix around the Y axis with a given angleψ , and tz

is the translation on the Z axis. The rotation and the translation parameters are

provided by the ego-car odometry. It is considered that the translations on the X and

Y axis are zero.

3.3 Data Association

This stage consists in finding the corresponding contours that identify a single object

in consecutive frames. As each extracted contour describes an Elevation Map blob,

finding the associated contour pairs is reduced to find a similarity between the object

blobs.

Fig. 4. The association between two set of blobs in the consecutive frames and the resulting set

of associated pairs.

For each object Pi from the previous frame and for each object Cj from the current

frame we calculate an overlapping score Aij. The results are stored into a score matrix

A={Aij}. Candidates with the highest score are taken into account in determining the

associations between the two set of objects P and C.

However the association problem may lead only to partial results in the cases when

larger objects from the previous frame are split into smaller blobs in the current frame

and vice versa. In order to find all possible pairs of candidates we perform two types

of associations: a direct association (forward association) finding best overlapping

candidates in the current frame for all blobs in the previous frame, and a reverse

association (backward association) that finds best overlapped objects in the previous

frame for all objects from the current frame (see Fig.4). The final list of candidates

includes all distinct pairs associated in the two steps.

4 Motion Estimation

The object motion estimation module receives as input a list of associated contour

pairs. For each distinct pair we compute correspondences between the two contours

and estimate a rotation and a translation which minimize the alignment error. For the

contour pairwise registration we use the Iterative Closest Point (ICP) method. The

ICP algorithm was proposed by Besl and McKay [14] and represents a common

solution especially for scan-matching techniques, but the idea could be adapted for

any kind of models.

For each contour pair that identifies the same object in the consecutive frames we

define two set of points: a model set P={p1,p2, ..., pM} that describes the object

contour in the previous frame, and a data set Q={q1,q2, ..., qK} that describes the

object contour in the current frame. For each point qj from Q the corresponding

closest point pi from P is found. We want to find an optimal rotation R and translation

T that minimize the alignment error. The objective function is defined:

∑=

−+=N

i

ii qTRpTRE1

2),(

(3)

where pi and qi are the corresponding point pairs of the two sets and N is the total

number of correspondences.

The proposed alignment method is described by the following main steps:

1. Matching – for each point from data set, the closest point from the model set is

found. A list of correspondent pairs is generated.

2. Outliers Rejection – Rejecting the outliers that could introduce a bias in the

estimation of translation and rotation.

3. Error Minimization – estimating new transformation parameters R and T for the

next iteration.

4. Updating – having the new R and T, a new target set is computed by applying the

new transformation to the model set. A global transformation Mg is updated with the

new R and T values.

5. Testing the convergence – compute the average point-to-point distance between

the measurement set and transformed model set. Then test if the algorithm has been

converged to a desired result. If the error is greater than a given threshold, the

process continues with a new iteration. The algorithm stops when the computed error

is below the selected error threshold or when a maximum number of iterations have

been achieved.

Next we will detail each of these steps.

4.1 Matching

At this stage, for each point qi from Q we want to find the closest point from the

model set P:

),(min),(}..1{

jiNj

i pqdPqdp∈

= (4)

Usually this task is the most computationally extensive in the ICP algorithm. The

classical brute force search approach has a complexity of )( pq NNO ⋅ , with Np being

the number of points in P and Nq – the number of points in Q. In order to reduce the

complexity to )log( pq NNO ⋅ many solutions employ a KD-Tree [21] data structure.

In our case, for finding closest points problem, we use a modified version of Chamfer

based Distance Transform [20] (see Fig. 5).

Fig. 5. Distance Transforms and Corresponding Masks are computed for dynamic obstacles

(left side), and for static obstacles (right side). Data contours (gray color) and model contours

(white color) are superimposed on the Distance Transform image. Each contour point in the

correspondence mask is labeled with a unique color. The colors in the corresponding mask

identify uniquely the closest contour point (having the same color).

A distance transform represents a map that has the property that each map cell has

a value proportional to the nearest obstacle point. In our case, for each separate model

contour we define a region of interest and compute the distance transform. The

difference of our solution is that we use two maps: a distance map that stores the

minimum distances to the closest points, and a correspondence map, storing the

positions of the closest points (see Fig. 5). The correspondences from the model set

are identified by superimposing the data contour on the two masks.

4.2 Outliers Rejection

The purpose of this stage is to filter erroneous correspondences that could influence

the alignment process. We use two types of rejection strategies: rejection of pairs

whose point-to-point distance is greater than a given threshold, and eliminating the

points where the overlap between the two contours is not complete.

4.2.1 Distance Based Rejection

The classical strategy consists in rejection of pairs whose point-to-point distance is

larger than a given threshold Dt:

tji Dpqd >),(

(5)

Because the stereo reconstruction error generally increases with the square of the z

distance, the stereo-system uncertainties must be taken into account. As suggested by

[10], if we assume that the stereo-vision system is rectified, then the z error is given

by the following relation:

fb

z dz

⋅

⋅=

σσ

2

(6)

Where z is the depth distance, b is the stereo system baseline; f is the focal length

and dσ denotes the disparity error. Thus, for each corresponding pair of points (pi,qi)

from the two sets, the rejection is made if:

ztji Dpqd σ+>),(

(7)

This would mean that the rejecting threshold is increased at once with the z

distance.

4.2.2 Boundary Based Rejection

The second type of rejecting is filtering the point correspondences caused by

incomplete overlap between contours. Usually, these situations appear when one of

the two contours is incompletely extracted due to occlusions, and may lead to

incorrect alignments. A possible solution is to identify the subsets of points from Q

that have the same correspondent point pj in P, and keeping only the pair with the

minimum distance (see Fig. 6).

Fig. 6. Rejecting the contour boundary.

4.3 Error minimization

In this step we determine the optimal rotation R and translation T by minimizing the

objective function defined by Equation (3).

The rotation matrix around the Y axis is linearized, approximating αcos by 1 and

αα ≈sin byα :

−

≈

−

=

10

010

01

cos0sin

010

sin0cos

)(

α

α

αα

αα

αyR

(8)

The translation vector is defined as:

[ ]Tzyx tttT = (9)

We can rewrite the Equation (3) as:

∑=

−

+

−

=N

i

zi

yi

xi

z

y

x

zi

yi

xi

q

q

q

t

t

t

p

p

p

TRE1

2

,

,

,

,

,

,

10

010

01

),(

α

α

(10)

The ),( TRE is minimized with respect toα , tx, ty, and tz by setting the partial

derivatives to zero:

( )

( )

( )

=−−+=∂

∂

=−+=∂

∂

=−++=∂

∂

=

+−−

++=

∂

∂

∑

∑

∑

∑

=

=

=

=

02),(

02),(

02),(

0)(

2),(

1

,,,,

1

,,,

1

,,,,

1 ,,,,,,

,,

2

,

2

,

N

i

zixizizi

z

N

i

yiyiyi

y

N

i

xizixixi

x

N

i xizizixixizi

zixizixi

qpptt

TRE

qptt

TRE

qpptt

TRE

pqpqpt

ptppTRE

α

α

α

α

(11)

Therefore we can obtain the unknown coefficients:

+−=

−=

−−=

−+

+−⋅

⋅

−

−+

=

∑∑∑

∑∑

∑∑∑

∑∑

∑ ∑∑ ∑

∑ ∑∑

===

==

===

==

= == =

= ==

N

i

xi

N

i

zi

N

i

ziz

N

i

yi

N

i

yiy

N

i

zi

N

i

xi

N

i

xix

N

i

xizi

N

i

zixi

N

i

N

i

xizi

N

i

N

i

zixi

N

i

N

i

zi

N

i

xizixi

ppqN

t

pqN

t

ppqN

t

pqpqN

qpqp

ppppN

1

,

1

,

1

,

1

,

1

,

1

,

1

,

1

,

1

,,

1

,,

1 1

,,

1 1

,,

1

2

1

,

2

1

,

2

,

2

,

1

1

1

)()(

)(

1

α

α

α

(12)

4.4 Updating

Assuming that we have estimated new R and T parameters in the previous step, a new

target set is computed by applying the new transformation to the model set.

Having the rigid body transformation matrix M:

−=

=

1000

10

010

01

10 z

y

x

t

t

t

TRM

α

α

(13)

Each point pi from the model set P is transformed according to the following

relation:

−=

+

+

+

11000

10

010

01

1

,

,

,

1

,

1

,

1

,

k

zi

k

yi

k

xi

z

y

x

k

zi

k

yi

k

xi

p

p

p

t

t

t

p

p

p

α

α

(14)

Finally, a global transformation MG is updated:

MMMk

G

k

G ⋅=+1 (15)

4.5 Testing the convergence

The error metric is estimated by computing the average Euclidean distance (AED) of

every corresponding pair of data set Q and transformed model set.

∑=

−=N

i

ii qpN

Err1

1

(16)

If the error is greater than a given threshold, the process continues with a new

iteration. The algorithm stops when the computed error is below the selected error

threshold or when a maximum number of iterations have been achieved.

5 Experimental Results

The proposed dynamic environment representation method has been tested in

different traffic situations. For our experiment we used a 2.66GHz Intel Core 2 Duo

Computer with 2GB of RAM. Fig. 7 presents some qualitative results obtained in a

dynamic urban traffic scenario.

Fig. 7. a) An urban traffic scenario. b) The alignment result (red color) between the model

delimiter extracted in previous frame (yellow) and the data contour, extracted in the current

frame (blue). c) The virtual view of the scene. The static obstacles are represented with green

delimiters while the dynamic obstacles are colored with red. The speed vectors are associated to

each dynamic entity. d) The representation result, projected on the left camera image.

In Fig. 7.b the model delimiter that was extracted in previous frame is colored with

yellow, while the data contour (extracted in the current frame) is drawn with blue.

The result of the alignment is illustrated with red color. It can be observer that in the

case of the incoming vehicle, as well as for the lateral static vehicles, the aligned

model is superimposed almost perfectly on the data set. In the Fig. 7.c, the virtual

view of the scene is shown. The static obstacles are represented with green delimiters

while the dynamic obstacles are colored with red. The speed vectors are associated to

the each dynamic entity (yellow color). The representation result is also projected on

the left camera image (see Fig. 7.d). We considered that the obstacles with a speed

greater than 8km/h are dynamic.

Fig. 8 shows a comparative result between the ICP algorithm that includes all

correspondence points (blue color) and the alignment method that uses the Contour

Boundary Rejection strategy (red color). We used the Average Euclidean Distance

(AED) as the error metric. It can be observed that the ICP algorithm based on

Boundary Rejection strategy converge more quickly than the ICP method without a

filtering mechanism and proves to be more accurate having a lower alignment error.

For our experiments we used a maximum number of 10 iterations. The average

processing time was about 38 ms.

Fig. 8. The computed Error Metric in the case of ICP algorithm that does not use outlier

rejection and ICP method that uses a Boundary Rejection.

6 Conclusions

In this paper we propose a method of real-time representation of the dynamic

environment by using the pairwise alignment of free-form models. Instead of

registering the whole 3D point cloud, the most visible obstacle points from the ego car

are extracted and are subjected to the alignment process. We extend the classical ICP

algorithm with a set of preprocessing tasks. First, we associate the delimiters at the

blob level. Then, a list of associated candidates is passed to the alignment stage. For

the registration process we use free-form polygonal models that minimize the

erroneous results caused by occlusions, or by stereo reconstruction errors. As future

work we propose to improve the stability of the environment perception by extending

our system with a temporal filtering of the estimated speeds.

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